# What is the domain and range of y=log_2x?

Jul 31, 2017

Domain: $\left(0 , \infty\right)$

Range: $\mathbb{R}$

#### Explanation:

First, remember that you cannot take $\log \left(0\right)$ and you cannot take the logarithm of a negative number and get a real number

So, $x > 0 \implies x \in \left(0 , \infty\right)$ which is our domain

Also, by the definition of ${\log}_{2} x$

$y = {\log}_{2} x$

$\iff$

${2}^{y} = x$

which is defined for all real numbers $\left(\mathbb{R}\right)$ , which gives us our range